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If 1/log₃ π + 1/log₄ π >x, then x will be

1) 1 2) 2 3) 4 4) none of these Solution: We know logb a = log a/logb Given 1/log3 π + 1/log4 π >x Let k = (log 3/log... View Article

The minimum value of 2 log₁₀ x – log_x0.01, x>1 is

1) 2 2) 4 3) 6 4) 8 Solution: 2 log10 x - logx 0.01 = 2 log10 x - (logx (1/102) = 2 log10 x + 2 logx 10 = 2log10 x + 2/log10 x) =... View Article

If log a = ½ log b = ⅕ log c, then a⁴b³c^-2 =

1) 1 2) 2 3) 3 4) 4 Solution: Let log a = ½ log b = ⅕ log c = k => log a = k, so a = ek log b = 2k, so b = e2k log c =... View Article

If a, b, c are distinct positive numbers, each different from 1, such that [log_b a log_c a – log_a a] + [log_a b log_c b – log_b b] + [log_a c log_b c – log_c c] = 0, then abc =

1) 1 2) 2 3) 3 4) 4 Solution: We use the property logn m = log m/log n Given [logb a logc a - loga a] + [loga b logc b - logb... View Article

If log x/(b – c) = log y/(c – a) = log z/(a – b), then which of the following is true.

1) xyz = 1 2) xaybzc = 1 3) xyz = xaybzc 4) none of these Solution: Let log x/(b - c) = log y/(c - a) = log z/(a - b) = k => log... View Article

If log₅ log₅ log₂ x = 0, then value of x is

1) 32 2) 125 3) 625 4) 25 Solution: Given log5 log5 log2 x = 0 => log5 log2 x = 1 => log2 x = 5 => x = 25 = 32 Hence... View Article

A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is

1) 9 h 2) 7.5 h 3) 6.5 h 4) 8 h Answer: 2) 7.5 h Solution: W be the velocity of water and M be the velocity of the motorboat in... View Article

If the order of two vectors A and B is reversed, then in the cross product of two vectors, the resultant vector

1) changes only in the direction 2) changes in magnitude 3) magnitude and direction 4) does not change both in magnitude and direction... View Article

If the angle between the vectors A and B is 0, then the value of the product (B × A) • A is equal to

1) BA2 cos θ 2) BA2 sin θ 3) BA2 sin θ cos θ 4) zero Answer: 4) zero Solution: (B x A) is perpendicular to... View Article

The sum of two vectors A and B is at right angle to their difference. Then,

1) A = B 2) A = 2B 3) B = 2A 4) A and B have the same direction Answer: 1) A = B Solution: Sum of two vectors r1 = A + B Difference of two... View Article

If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle between the two vectors is

1) 45° 2) 90° 3) 180° 4) 360° Answer: 1) 45° Solution: |A - B| = |A x B| tan θ = 1 tan θ =... View Article

The coordinates of a particle moving in XY-plane at any instant of time t are x = 4t², y = 3t². The speed of the particle at that instant is

1) 10 t 2) 5 t 3) 3 t 4) 2 t 5) √13t Answer: 1) 10 t Solution: x = 4t2 Differentiating w.r.t t Vx = (dx/dt) = 8t y =... View Article

The value of lim_x→0 (cos x)^{cot^(2) x} is

1) e-1 2) e-1/2 3) 1 4) does not exist Solution: (2) e-1/2... View Article

The value of lim_x→1 [sin (e^x-1 – 1)] / log x =

1) 0 2) e 3) 1/e 4) 1 Solution: (4) 1... View Article

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Archives

If 1/log₃ π + 1/log₄ π >x, then x will be

The minimum value of 2 log₁₀ x – log_x0.01, x>1 is

If log a = ½ log b = ⅕ log c, then a⁴b³c^-2 =

If a, b, c are distinct positive numbers, each different from 1, such that [log_b a log_c a – log_a a] + [log_a b log_c b – log_b b] + [log_a c log_b c – log_c c] = 0, then abc =

If log x/(b – c) = log y/(c – a) = log z/(a – b), then which of the following is true.

If log₅ log₅ log₂ x = 0, then value of x is

A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is

If the order of two vectors A and B is reversed, then in the cross product of two vectors, the resultant vector

If the angle between the vectors A and B is 0, then the value of the product (B × A) • A is equal to

The sum of two vectors A and B is at right angle to their difference. Then,

If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle between the two vectors is

For the vectors A and B making an angle θ. Which one of the following relations is correct?

Vector A has a magnitude of 5 units lies in the XY- plane

Two equal vectors have a resultant equal to either of them, then the angle between them will be

Two equal forces (P each) act at a point inclined to each other at an angle of 120°. The magnitude of their resultant is

Three concurrent coplanar forces 1 N, 2 N and 3 N acting along different directions on a body

The square of resultant of two equal forces is three times their product. Angle between the forces is

The coordinates of a particle moving in XY-plane at any instant of time t are x = 4t², y = 3t². The speed of the particle at that instant is

The value of lim_x→0 (cos x)^{cot^(2) x} is

The value of lim_x→1 [sin (e^x-1 – 1)] / log x =

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